The 26-year-old joined from Dutch side VVV-Venlo on transfer deadline day but - more than three weeks later - is still waiting to make his first appearance for the Glasgow club as he has been busy building up his fitness.
Giakoumakis scored 26 goals as he finished top scorer in the Eredivisie last term and Celtic supporters are likely to get their first glimpse of the new man against Raith, possibly as a substitute.
Postecoglou said: "He'll be part of the squad for Raith. It'll be his first game of the season so we don't expect him to come in and be flying. Like every player, it's going to take him a bit of time to get up to speed and get some match fitness.
"The good thing is that he's had a good, solid week of training and he feels pretty good. We'll hopefully get him some game time against Raith and then build from there."
Postecoglou could do with the new man making an impact in the coming weeks as he is still without several key players, including captain Callum McGregor, Kyogo Furuhashi, Greg Taylor, James Forrest and Christopher Jullien.
The manager insists his team simply have to find a way of battling through this testing period.
He said: "I'm not a woe-is-me kind of bloke. It would be great to have a full complement of players. We're obviously missing our skipper and our top scorer and you can start thinking things are piling up against you or you can see it as an opportunity to build resilience.
"Things will settle down. The key thing is that we stay calm and stay strong. You can go around thinking about the possibilities if you had everyone available but that's not in our control.
What is in our control is that we have a game on Thursday night and an opportunity to progress in a competition and that's where our focus is."
Postecoglou hopes to have Forrest and Jullien - who has been out since last December - back in contention next month.
He said: "I think after the international window I'd expect both of them to hopefully be training with the first team. After that, it will depend on their levels of fitness and how quickly they adapt to what we want to do with our football."